An ac current is represented as i = 5√2 + 10cos(650πt + π/6) Amp. The r.m.s value of the current is

The correct answer is Option 2. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Physics Q35 – JEE-MAIN 2025

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Home Physics Alternating CurrentQuestion #16

An ac current is represented as

i = 5 \sqrt{2} + 10 \cos (650 π t + \frac{π}{6})

Amp The r.m.s value of the current is

Clue 1 of 3: Recognize the components

The given current waveform consists of both a DC component and an AC sinusoidal component.

🧠 Full Solution Path

Step 1: Identify DC and AC Components✦ Active

The given current equation is $i = 5 \sqrt{2} + 10 \cos (650 π t + \frac{π}{6})$ . This can be separated into a DC component and an AC component.

I_{D C} = 5 \sqrt{2} Amp

i_{A C} = 10 \cos (650 π t + \frac{π}{6}) Amp

Step 2: Calculate RMS Values for Each Component○ Expand

The RMS value of the DC component is simply the DC value itself. For the AC component, the peak value is $I_{m} = 10$ Amp. The RMS value of a sinusoidal AC current is $I_{R M S, A C} = \frac{I_{m}}{\sqrt{2}}$ .

I_{R M S, D C} = I_{D C} = 5 \sqrt{2} Amp

I_{R M S, A C} = \frac{10}{\sqrt{2}} = 5 \sqrt{2} Amp

💡 Teacher's Secret Hint

Remember that the RMS value of a DC current is the current itself.

Step 3: Combine RMS Values for Total Current○ Expand

For a current containing both DC and AC components, the total RMS value is given by the formula $I_{R M S} = \sqrt{I_{R M S, D C}^{2} + I_{R M S, A C}^{2}}$ .

I_{R M S} = \sqrt{(5 \sqrt{2})^{2} + (5 \sqrt{2})^{2}}

I_{R M S} = \sqrt{(25 \times 2) + (25 \times 2)}

I_{R M S} = \sqrt{50 + 50}

I_{R M S} = \sqrt{100}

I_{R M S} = 10 Amp

💡 Teacher's Secret Hint

Ensure you square the individual RMS values before adding them, then take the square root.

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Physics Question 35 – JEE-MAIN 2025

Clue 1 of 3: Recognize the components

🧠 Full Solution Path